Chapter 1
Chapter 2
Chapter 3

Are these scenarios inferential and descriptive?

1) A teacher calculates the average, median, and standard deviation of math test scores for a class to summarize and describe the overall performance. 

2) A company compares the productivity of employees who received a new training program with those who did not, using a sample to make inferences about the impact on the entire employee population.

1) Descriptive 

2) Inferential 


Calculate the mean of the following dataset: 10, 15, 20, 25, 30

Mean = 20


What could be a third variable in this scenario: 

A researcher is examining the correlation between the amount of time students spend on social media and their academic performance. 

In this scenario, a third variable could be the students' sleep quality. It's plausible that students who spend more time on social media may have poorer sleep quality, and both social media use and sleep quality could independently affect academic performance.


Describe Unimodal, Bimodal, and Multimodal.

  • Unimodal is a distribution or dataset with one distinct peak or mode. There is one value that occurs more frequently than any other.
  • Bimodal is a distribution or dataset with two distinct peaks or modes. Two values that occur more frequently than others, creating two separate modes.
  • Multimodal is a distribution or dataset with more than two distinct peaks or modes.

For each scenario identify the variable of measurement used.

1) A university is conducting a survey to gather data on the majors chosen by its students.

2) A restaurant is collecting feedback on customer satisfaction with its service

3) A company is measuring employee engagement using a survey with a Likert scale.

4) A fitness trainer tracks the amount of weight lifted by clients during strength training sessions.

1) Nominal 

2) Ordinal 

3) Interval

4) Ratio 


Turn this z-score into a raw score: 

In a standardized IQ test, the mean IQ score is 100, and the standard deviation is 15. Sarah's IQ score is 125. 

Raw Score = 125


 Identify the Relationship of a Scatterplot:

 The scatterplot reveals a downward trend, with higher weekly running distances corresponding to lower weights. This indicates a negative correlation, suggesting that individuals who run more kilometers per week tend to have lower weights.


What is a Mean, Median, & Mode?

  • Mean is the average of a set of values, is calculated by summing them and dividing by the number of values.
  • Median is the middle value in a dataset when all values are arranged in ascending order. It is not influenced by extreme values.
  • Mode is the value that appears most frequently in a dataset. There are three or more values that occur with relatively high frequency, resulting in multiple modes.

Identify the variables, values, and scores in this scenario:

A teacher is conducting a quiz in a math class, and each student receives a score.

  • Variables = Quiz scores
  • Values = Any numerical scores i.e., 85, 92, 78
  • Scores = The actual results obtained by each student (e.g., 85, 92, 78) representing their performance on the quiz.

Interpret the results of this study: 

A correlational study is conducted to examine the relationship between the frequency of outdoor activities and levels of stress in a sample of adults. The correlation coefficient (r) is found to be -0.75.

This indicates a strong negative correlation, implying that as the frequency of outdoor activities increases, stress levels tend to decrease. However, it's important to note that this does not imply a cause-and-effect relationship; other factors could contribute to this observed correlation.


If we find a correlation coefficient of 0.8 between the number of hours spent studying and the exam scores what does this mean?

It means that as the number of study hours increases, the exam scores tend to increase as well. This positive correlation suggests that studying more is associated with higher exam scores.


What is correlation and regression?

  • Correlation is a statistical measure indicating the extent to which two variables change together.
  • Regression is a statistical method used to examine the relationship between two or more variables, often to predict one variable based on the values of others.

Describe the shape of the distribution of study hours and identify any potential outliers:

In a statistics class, students were asked about the number of hours they spent studying for the final exam. The following data represents the study hours reported by each student: 4, 6, 8, 10, 12, 12, 14, 16, 18, 20.

The distribution of study hours appears to be positively skewed, as most students reported lower study hours, with only a few reporting higher values. Most students spent between 4 to 14 hours studying.


Find the z-score in this scenario:

Suppose you have a dataset of exam scores from a class of students. The mean (average) exam score is 75, and the standard deviation is 8. You want to find the z-score for a student who scored 82 on the exam.

The z-score for the student who scored 82 on the exam is approximately 0.875. 



Explain the result of this correlational study: 

After analyzing the data, the researcher finds a positive correlation of 0.75 between the hours of exercise per week and the level of physical fitness. This correlation coefficient suggests a moderately strong positive relationship between the two variables.

Individuals who spend more time exercising tend to have higher levels of physical fitness, and those who exercise less tend to have lower levels of physical fitness.


What is Standard Deviation?

  • Standard deviation is a measure of the amount of variation or dispersion in a set of values, indicating how much individual values differ from the mean.

A teacher wants to create a frequency table for the number of candies students have in their lunchboxes in third-grade class. Here is the data for the number of candies reported by each student: 2, 3, 2, 4, 3, 1, 2, 3

*pull screenshot of frequency table*


What does the z-score in this scenario mean:

The mean height for students in a school is 160 cm, with a standard deviation of 10 cm. Now, if a student named Alex has a height of 175 cm his z-score is 1.5. 

The z-score of 1.5 indicates that Alex's height is 1.5 standard deviations above the mean height of the students in the school. This suggests that Alex is relatively taller compared to the average height of the students.


Calculate the correlation coefficient with the given data

 * note to self, pull up rainbow table*

R= -0.98


What is variance?

  • Variance is a statistical measure of the spread or dispersion of a set of values, calculated as the average of the squared differences from the mean.